JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A =\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)\) and \(B =\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)\). Then the number of elements in the set \(\left\{( n , m ): n , m \in\{1,2, \ldots . .10\}\right.\) and \(\left.nA ^{ n }+ mB ^{ m }= I \right\}\) is
- A \(1\)
- B \(3\)
- C \(5\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(A ^{2}= A\) and \(B ^{2}= B\) Therefore equation \(nA ^{ n }+ mB ^{ m }= I\) becomes \(nA + mB = I\), which gives \(m = n =1\) Only one set possible
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